Average Error: 28.2 → 28.2
Time: 49.4s
Precision: 64
Internal Precision: 128
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.2

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.2

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.2

    \[\leadsto \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

Details

Time bar (total: 42.2s)Debug log

start102.0ms

Algorithm
intervals

setup185.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize54.0ms

Local error

Found 4 expressions with local error:

32.5b
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
0.1b
(* (+ (* x y) z) y)
0.1b
(* (+ (* (+ (* (+ y a) y) b) y) c) y)

rewrite74.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

34.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
24.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
9.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)

series500.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

347.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
68.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
49.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
37.0ms
(* (+ (* x y) z) y)

simplify7.0s

Counts
53 → 82
Calls

53 calls. Slowest were:

503.0ms
(* (+ (pow (* (+ (* (+ y a) y) b) y) 3) (pow c 3)) y)
351.0ms
(* (+ (pow (* (+ (* x y) z) y) 3) (pow 27464.7644705 3)) y)
333.0ms
(+ (pow (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) 3) (pow t 3))

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 31.7b

localize9.0ms

Local error

Found 4 expressions with local error:

31.9b
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
0.7b
(/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
0.1b
(* (+ (* x y) z) y)

rewrite89.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

43.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
18.0ms
(/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
18.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)

series451.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

318.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
64.0ms
(/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
47.0ms
(* (+ (* (+ (* x y) z) y) 27464.7644705) y)
22.0ms
(* (+ (* x y) z) y)

simplify7.9s

Counts
46 → 83
Calls

46 calls. Slowest were:

1.1s
(* (+ (pow (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) 3) (pow t 3)) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
624.0ms
(* (+ (pow (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) 3) (pow t 3)) 1)
418.0ms
(* (- (* (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)) (* t t)) 1)

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 31.7b

localize28.0ms

Local error

Found 4 expressions with local error:

28.5b
(/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
0.1b
(* (+ (* 27464.7644705 y) 230661.510616) y)
0.1b
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
0.1b
(* (+ (* (+ y a) y) b) y)

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

25.0ms
(/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
14.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
12.0ms
(* (+ (* (+ y a) y) b) y)

series260.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

128.0ms
(/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
53.0ms
(* (+ (* (+ (* (+ y a) y) b) y) c) y)
45.0ms
(* (+ (* 27464.7644705 y) 230661.510616) y)
32.0ms
(* (+ (* (+ y a) y) b) y)

simplify6.2s

Counts
53 → 82
Calls

53 calls. Slowest were:

453.0ms
(* (+ (pow (* (+ (* (+ y a) y) b) y) 3) (pow c 3)) y)
349.0ms
(sqrt (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
330.0ms
(* (- (* (* (+ (* (+ y a) y) b) y) (* (+ (* (+ y a) y) b) y)) (* c c)) y)

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 31.4b

localize19.0ms

Local error

Found 4 expressions with local error:

28.5b
(/ (+ (* (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) (cbrt (+ (* 27464.7644705 y) 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
1.7b
(cbrt (+ (* 27464.7644705 y) 230661.510616))
1.7b
(cbrt (+ (* 27464.7644705 y) 230661.510616))
1.7b
(cbrt (+ (* 27464.7644705 y) 230661.510616))

rewrite102.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

93.0ms
(/ (+ (* (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) (cbrt (+ (* 27464.7644705 y) 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
2.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))
2.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))

series280.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

96.0ms
(/ (+ (* (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) (cbrt (+ (* 27464.7644705 y) 230661.510616))) (* (cbrt (+ (* 27464.7644705 y) 230661.510616)) y)) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
73.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))
60.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))
51.0ms
(cbrt (+ (* 27464.7644705 y) 230661.510616))

simplify8.8s

Counts
56 → 82
Calls

56 calls. Slowest were:

453.0ms
(- (+ (pow 230661.510616 1/3) (+ (* 0.0396898531780084 (* y (pow 230661.510616 1/3))) (* 0.0007876422226459316 (* (pow y 2) (pow 230661.510616 1/3))))) (* 125718881.23667318 (* (pow y 2) (pow (/ 1 (pow 230661.510616 5)) 1/3))))
420.0ms
(- (+ (pow 230661.510616 1/3) (+ (* 0.0396898531780084 (* y (pow 230661.510616 1/3))) (* 0.0007876422226459316 (* (pow y 2) (pow 230661.510616 1/3))))) (* 125718881.23667318 (* (pow y 2) (pow (/ 1 (pow 230661.510616 5)) 1/3))))
391.0ms
(+ (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) (* (+ (* (+ (* (+ y a) y) b) y) c) y)) (- (* i i) (* (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

prune2.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 31.4b

regimes2.2s

Accuracy

0% (1.0b remaining)

Error of 28.2b against oracle of 27.3b and baseline of 28.2b

bsearch10.0ms